Problem: Express this quotient in scientific notation: ${\frac{1.020\times 10^{3}} {6.0\times 10^{5}}}$
Start by collecting like terms together. $= {\frac{1.020} {6.0}} \times{\frac{10^{3}} {10^{5}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.17 \times 10^{3\,-\,5}$ $= 0.17 \times 10^{-2}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.17$ is the same as $1.70 \div 10$ , or $1.70 \times 10^{-1}$ $ = {1.70 \times 10^{-1}} \times 10^{-2} $ $= 1.70\times 10^{-3}$